On formality of Sasakian manifolds



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Biswas, Indranil and Fernandez, Marisa and Muñoz, Vicente and Tralle, Aleksy (2016) On formality of Sasakian manifolds. Journal of Topology, 9 (1). pp. 161-180. ISSN 1753-8416

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Official URL: http://jtopol.oxfordjournals.org/content/early/2016/01/07/jtopol.jtv044.abstract#


We investigate some topological properties, in particular formality, of compact Sasakian manifolds. Answering some questions raised by Boyer and Galicki, we prove that all higher (than three) Massey products on any compact Sasakian manifold vanish. Hence, higher Massey products do obstruct Sasakian structures. Using this, we produce a method of constructing simply connected K-contact non-Sasakian manifolds. On the other hand, for every n > 3, we exhibit the first examples of simply connected compact Sasakian manifolds of dimension 2n + 1 that are non-formal. They are non-formal because they have a non-zero triple Massey product. We also prove that arithmetic lattices in some simple Lie groups cannot be the fundamental group of a compact Sasakian manifold.

Item Type:Article
Uncontrolled Keywords:Sasakian manifold; Formality; Massey product.
Subjects:Sciences > Mathematics > Geometry
ID Code:37572
Deposited On:11 May 2016 11:17
Last Modified:12 Dec 2018 15:12

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